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18
SCNN: A Universal Simulator for Cellular Neural Networks
 Proc. IEEE CNNA 96
, 1996
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A Learning Algorithm For Cellular Neural Networks (CNN) Solving Nonlinear Partial Differential Equations
 Proc. ISSSE 95
, 1995
"... A learning procedure for CNN is presented and applied in order to find the parameters of networks approximating the dynamics of certain nonlinear systems which are characterized by partial differential equations (PDE). Our results show that  depending on the training pattern  solutions of vari ..."
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Cited by 6 (3 self)
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A learning procedure for CNN is presented and applied in order to find the parameters of networks approximating the dynamics of certain nonlinear systems which are characterized by partial differential equations (PDE). Our results show that  depending on the training pattern  solutions of various PDE can be approximated with high accuracy by a simple CNN structure. Results for two nonlinear PDE, Burgers' equation and the Kortewegde Vries equation, are discussed in detail. 1. INTRODUCTION A CNN [2,3,4] is a system of simple nonlinear processors (cells) which are arranged in one or more layers on a regular grid. Interactions between cells are local and usually translation invariant, i.e. a connection from a cell j towards another cell i only exists if j is part of i's neighborhood N (i) and its type and strength depend only on the relative position of j with respect to i. Thus the number of connections increases only linearly with the number of cells, a feature that makes hardwa...
An Exact and Direct Analytical Method for the Design of Optimally Robust CNN Templates
 IEEE TRANS. CIRCUITS & SYST.I
, 1999
"... In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNN's) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all welldefined CNN tasks are characterized by a ..."
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Cited by 5 (2 self)
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In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNN's) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all welldefined CNN tasks are characterized by a finite set of linear and homogeneous inequalities. This system of inequalities can be analytically solved for the most robust template by simple matrix algebra. For the relative robustness of a task, a theoretical upper bound exists and is easily derived, whereas the absolute robustness can be arbitrarily increased by template scaling. A series of examples demonstrates the simplicity and broad applicability of the proposed method.
Modeling Nonlinear Systems With Cellular Neural Networks
 Proc. ICASSP 96, Atlanta
, 1996
"... A learning procedure for the dynamics of cellular neural networks (CNN) with nonlinear cell interactions is presented. It is applied in order to find the parameters of CNN that model the dynamics of certain nonlinear systems, which are characterized by partial differential equations (PDE). Values of ..."
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Cited by 4 (4 self)
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A learning procedure for the dynamics of cellular neural networks (CNN) with nonlinear cell interactions is presented. It is applied in order to find the parameters of CNN that model the dynamics of certain nonlinear systems, which are characterized by partial differential equations (PDE). Values of a solution of the considered PDE for a particular initial condition are taken as the training pattern at only a small number of points in time. Our results demonstrate that CNN obtained with our method approximate the dynamical behaviour of various nonlinear systems accurately. Results for two nonlinear PDE, the \Phi 4 equation and the sineGordon equation, are discussed in detail. 1. INTRODUCTION CNN [1,2,3] form a special class of recurrent neural networks with the following distinguishing properties: ffl The cells, the states and outputs of which are given by real numbers, are placed in one ore more layers on a regular lattice usually of 1, 2 or 3dimensions. ffl Direct interacti...
A Learning Algorithm for the Dynamics of CNN with Nonlinear Templates  Part I: DiscreteTime Case
 Part I: DiscreteTime Case; Proc. CNNA96, S. 461466
, 1996
"... : A learning algorithm for the dynamics of discretetime cellular neural networks (DTCNN) with nonlinear templates gradientbased is presented. For modeling the dynamics of nonlinear spatiotemporal systems with DTCNN, it is applied to find the network parameters. Results for two different nonlinear ..."
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Cited by 4 (1 self)
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: A learning algorithm for the dynamics of discretetime cellular neural networks (DTCNN) with nonlinear templates gradientbased is presented. For modeling the dynamics of nonlinear spatiotemporal systems with DTCNN, it is applied to find the network parameters. Results for two different nonlinear timediscrete systems are discussed in detail. 1. Introduction Design and learning methods for cellular neural networks with linear template elements [1] have been studied by many authors [2, 3, 4]. In order to train fixpoints in both continuoustime and discretetime cellular neural networks (CNN and DTCNN), it was shown in these investigations, that the parameters of such networks can be determined by different gradient based methods. Up to now the determination of methods for training the dynamics of cellular neural networks with nonlinear interactions between the cells is an open problem. In previous papers [5, 6, 7] we have shown that by modeling continuoustime systems with CNN the ...
Adaptive Simulated Annealing in CNN Template Learning
, 1999
"... Introduction Opportunities for the application of template optimization (or "learning") for a Cellular Neural Network (CNN) [1] are prevalent insG hareas as pattern recognition andtexture clasturedG50G Itis highly des788Ed to employ an algorithm which not only can produce optimal simald0G ..."
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Cited by 4 (0 self)
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Introduction Opportunities for the application of template optimization (or "learning") for a Cellular Neural Network (CNN) [1] are prevalent insG hareas as pattern recognition andtexture clasturedG50G Itis highly des788Ed to employ an algorithm which not only can produce optimal simald0GT but which can als findthesdthed5 e#ciently, in as sGGG a timeas posM507d Various templatelearning methods have been propos6E5 date [2]. In [3] and[4], a hybridDirectSearch methodandSimulatedAnnealing (SA) were inves8F gatedforDisford00G6d CNN template optimization. Another algorithm, whichhas been widelyuse for CNN template learningtasni is the Genetic Algorithm (GA) [5], [6]. A variant of GA, from aclas calledEvolutionaryStrategies was appliedin [7] to obtain featureextraction templates Inthis letter, we compare the performance of a recentlydeveloped optimization algorithm called Adaptive Simulated Annealing (ASA)agains GA. In a publisG87T8dsds sbl y, ASAsAd5TM5 outperformedGA on asG of
Analysis Of Cellular Neural Networks With Parameter Deviations
, 1997
"... In this paper the effect of parameter deviations on Cellular Neural Networks is considered. It will be shown that even small deviations can cause a significant misbehaviour of a network. Therefore a training method is presented for minimizing these influence and obtaining translation invariant templ ..."
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Cited by 3 (3 self)
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In this paper the effect of parameter deviations on Cellular Neural Networks is considered. It will be shown that even small deviations can cause a significant misbehaviour of a network. Therefore a training method is presented for minimizing these influence and obtaining translation invariant templates and a translation variant bias, which is well suited for hardware implementations with nonideal components. First results obtained with a hardware environment are shown. I. INTRODUCTION The dynamics of a multi layer Cellular Neural Network (CNN) [1,2,3] a system of nonlinear local interacting cells, can be determined for example by state equations of the form C dx m i (t) dt = \Gamma 1 R x m i (t) + M X m 0 =1 (1) X j2N m 0 m (i) A m 0 m i;j (y m 0 j (t); y m i (t)) + X j2N m 0 m (i) B m 0 m i;j (u m 0 j (t); u m i (t)) + X j2N m 0 m (i) A 0 m 0 m i;j (y m i (t \Gamma A ); y m 0 j (t \Gamma B )) + X j2N m 0 m (i) B 0 ...
SCNN 2000  Part II: The Simulation Control System
 in IEEE Int. Workshop on Cellular Neural Networks and Their Applications
, 2000
"... : In this paper the control system of SCNN 2000 [2], a universal simulation system for Cellular Neural Networks is introduced. It performs all inputoutput operations. The presented control system is based on the universal scripting language SCNNS, the SCNN shell and a graphical user interface. All ..."
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Cited by 2 (2 self)
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: In this paper the control system of SCNN 2000 [2], a universal simulation system for Cellular Neural Networks is introduced. It performs all inputoutput operations. The presented control system is based on the universal scripting language SCNNS, the SCNN shell and a graphical user interface. All three subsystems are necessary for a full functionality of SCNN 2000. The different parts of the control system, followed by examples of 3dimensional modelling applications of the control system will be discussed in detail. 1. Introduction Since the first introduction of SCNN in 1996 [12] various extensions have been implemented, e.g. an extended external programmability, which allow functional extensions easily. Furthermore, a modern graphical user interface and a powerful shell environment has been added. Therefore an external scripting language SCNNS has been developed and firstly introduced in an early version of SCNN 4 [3]. In SCNN 2000 beside all old features a new improved functiona...
A Recurrent Fuzzy Cellular Neural Network System with Automatic Structure and Template Learning
 IEEE Trans. On Circuits and SystemsI
"... Abstract—It is widely accepted that using a set of cellular neural networks (CNNs) in parallel can achieve higher level information processing and reasoning functions either from application or biologics points of views. Such an integrated CNN system can solve more complex intelligent problems. In ..."
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Abstract—It is widely accepted that using a set of cellular neural networks (CNNs) in parallel can achieve higher level information processing and reasoning functions either from application or biologics points of views. Such an integrated CNN system can solve more complex intelligent problems. In this paper, we propose a novel framework for automatically constructing a multipleCNN integrated neural system in the form of a recurrent fuzzy neural network. This system, called recurrent fuzzy CNN (RFCNN), can automatically learn its proper network structure and parameters simultaneously. The structure learning includes the fuzzy division of the problem domain and the creation of fuzzy rules and CNNs. The parameter learning includes the tuning of fuzzy membership functions and CNN templates. In the RFCNN, each learned fuzzy rule corresponds to a CNN. Hence, each CNN takes care of a fuzzily separated problem region, and the functions of all CNNs are integrated through the fuzzy inference mechanism. A new online adaptive independent component analysis mixturemodel technique is proposed for the structure learning of RFCNN, and the orderedderivative calculus is applied to derive the recurrent learning rules of CNN templates in the parameterlearning phase. The proposed RFCNN provides a solution to the current dilemma on the decision of templates and/or fuzzy rules in the existing integrated (fuzzy) CNN systems. The capability of the proposed RFCNN is demonstrated on the realworld defect inspection problems. Experimental results show that the proposed scheme is effective and promising. Index Terms—Cellular neural networks (CNN) template design, defect inspection, fuzzy clustering, fuzzy neural network (FNN), independent component analysis (ICA), ordered derivative, recurrent neural network. I.
Learning Algorithms For Cellular Neural Networks
 in Proc. IEEE Int. Symp. Circuits Systems
, 1998
"... A learning algorithm based on the decomposition of the Atemplate into symmetric and antisymmetric parts is introduced. The performance of the algorithm is investigated in particular for coupled CNNs exhibiting diffusionlike and propagating behavior. 1. INTRODUCTION Cellular neural networks (CN ..."
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A learning algorithm based on the decomposition of the Atemplate into symmetric and antisymmetric parts is introduced. The performance of the algorithm is investigated in particular for coupled CNNs exhibiting diffusionlike and propagating behavior. 1. INTRODUCTION Cellular neural networks (CNNs) are examples of recurrent networks defined by the following system of differential equations dx ij (t) dt =x ij (t) + # mn#N ij amn y mn (t) + # mn#N ij bmn u mn + I , where N ij denotes the neighborhood of the ijth cell for 1 # i # M,1# j # N and y = (x +1x 1)/2 . The state, input and output of a cell are defined by x ij , u ij and y ij , respectively. We assume a nearest neighborhood CNN. The output at an equilibrium point, when one exists, is denoted by y # ij .The parameters of a CNN are gathered into the socalled Atemplate, the Btemplate and the bias I. In view of learning algorithms, since a CNN is a recurrent neural network, one can apply the lea...